If a nonlinear system depends on a parameter, then the equilibrium points can change as the parameter varies. In other words, as the parameter changes, a bifurcation can occur. Consider the one-parameter system family of systems dx = x2 – a =-y(+2+1), where a is the parameter.(a) Show that the system has no equilibrium points if a < 0. (b) Show that the system has two equilibrium points if a > 0. (c) Show that the system has exactly one equilibrium point if a = 0. (d) Find the linearization of the equilibrium point for a = 0 and compute the eigenvalues of this linear system.

Answers

Answer 1

If a<0, then there is no x-null lines, the system has no equilibrium points.

If a=0, it has only one equilibrium points.

If a>0, the system has two equilibrium points.

Points are (-√a,0) and (√a,0)

The system changes from no fixed points to two fixed points when it increases through a=0.

a is a bifurcation point.

The Jawbian matrix,

                        J = [tex]\left[\begin{array}{ccc}2x&0\\-2xy&x^{2}-1\\\end{array}\right][/tex]

Now,

      J[0,0] = [tex]\left[\begin{array}{ccc}0&0\\0&-1\\\end{array}\right][/tex] =0

      J[-√a,0] = [tex]\left[\begin{array}{ccc}-2\sqrt{a} &0\\0&-a-1\\\end{array}\right][/tex] = 2a√a + 2√a

If a=0, then it will be a live equilibrium, one of the values are 0, For a>0, the point (-√a,0) is sink and (√a,0) is a saddle points.

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Related Questions

Find the constant term in the expansion of (2x+1/x)8

Answers

Answer:

the constant term in this problem is 8

I’m pretty sure it’s 8 !!

Find the solution to the system by substitution

y=2x-1
x-2y=-1

Answers

Answer:

x = 1

y = 1

Step-by-step explanation:

Substitute y with 2x-1:

x - 2(2x-1) = -1

x - 4x + 2 = -1

-3x + 2 = -1

-3x = -1 - 2

-3x = -3

x = 1

Substitute x with 1

y = 2(1) - 1

y = 2 - 1

y = 1

7. suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. use the 68-95-99.7 rule to find the percentage of buyers who paid: a. between $147,700 and $152,300 if the standard deviation is $2300. b. more than $154,800 if the standard deviation is $2400.

Answers

a. 68 %  between $147,700 and $152,300 if the standard deviation is $2300

b. 2.5 % more than $154,800 if the standard deviation is $2400

Given that:

Prices of a certain model of a new home are normally distributed with a mean of $150,000.

Using the 68-95-99.7 rule ,  find the percentage of buyers who paid between $147,700 and $152,300 if the standard deviation is $2300.

Let X = prices of a certain model of a new home

SO, X ~ Normal ( μ = 150,000 , σ = 2,300 )

z score probability distribution for normal distribution

Z = X - μ / σ  

where μ population mean price = $150,000

σ  standard deviation = $2,300

According to 68-95-99.7 rule;

Around 68% of the values in a normal distribution lies between μ - σ and μ +σ .

Around 95% of the values occur between  μ - 2σ and μ + 2σ  .

Around 99.7% of the values occur between  μ - 3σ and μ + 3σ.

Find the z scores for both given values

Z = X - μ / σ  

  =   [tex]\frac{147,700 - 150,000}{2,300}\\ \\ \\[/tex]

 = -1

Z = X - μ / σ  

  = [tex]\frac{152,300 - 150,000}{2,300}[/tex]

 = -1

The z score indicates that the category of between  μ - σ and μ +σ .

Therefore , this represents that percentage of buyers who paid between $147,700 and $152,300 is 68%.

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Can someone help please? Picture is already attached

Answers

Answer:

-4 C

Step-by-step explanation:

Answer ASAP
Point R is at (3, 1.3) and Point T is at (3, 2.4) on a coordinate grid. The distance between the two points is
. (Input numbers and decimal point only, such as 8.2.) (3 points)

Answers

Answer:

1.1

Step-by-step explanation:

Math, help pls..................................

Answers

The measure of ∡ PRQ, if the sum of an interior angle of a triangle is  [tex]180^o[/tex] is  75°, so option B is correct.

What is the triangle?

One of the fundamental shapes in geometry is represented by the symbol Δ and consists of three connected vertices.

Given:

The lines m and n are parallel,

∡ QPR = 70°

As the lines are parallel, the alternate angles will be equal,

∡PQR  = ∡ QPN = 35°

The sum of the interior angles of the triangle is [tex]180^o[/tex]

∡ QPR  + ∡ PRQ + ∡ RQP = 180

70 + 35 + ∡ PRQ = 180

∡ PRQ = 180 - 105

∡ PRQ = 75°

Therefore, the measure of ∡ PRQ, if the sum of an interior angle of a triangle is [tex]180^o[/tex] is  75°.

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Simplify for all questions.

Answers

Answer:

3y; -2a; -5y; 3c; -6

-----------------------------------------

Question 1[tex]-\sqrt{9y^2}=-(-3y)= 3y, \ since\ y < 0[/tex]

Question 2[tex]0.5\sqrt{16a^2} =0.5(-4a)=-2a,\ since\ a < 0[/tex]

Question 3[tex]-5\sqrt{y^2} =-5y, since \ y > 0[/tex]

Question 4[tex]3\sqrt{c^2} =3c,\ since \ c \geq 0[/tex]

Question 5[tex]\sqrt{(3-\sqrt{15})^2 } -\sqrt{(3+\sqrt{15})^2 } =-(3-\sqrt{15}) -(3+\sqrt{15})=-6, since\ 3 < \sqrt{15}[/tex]

Work out the value of d in the equality below. 0.0043 = 4.3 × 10d​

Answers

Answer:

d= -3

Step-by-step explanation:

Rearrange variables to the left side of the equation: -4.3x 10d= -0.0043

Divide both sides of the equation by the coefficient of variable

Reduce the fraction

Convert fraction into negative exponential form

Convert both sides of the equation into terms with the same with same base

Simplify using exponent power rule

Based on the given conditions, corresponding exponents are equal

triangle p undergoes a sequence of transformations resulting in tringle q. which sequence of transformation could be used to show that triangle q is similar but not congruent to triangle P

Answers

The transformation could be used to show that triangle Q is similar but not congruent to triangle P is Dilation.

What is transformation?

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.

Given that, triangle P undergoes a transformations resulting in triangle Q.

We know, Dilation would not change the shape, just the size; the angle measures would be the same, and the ratio of corresponding sides would be equal to the scale factor used in the dilation. This would give us a similar, but not congruent, figure.

Hence, The transformation could be used to show that triangle Q is similar but not congruent to triangle P is Dilation.

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A satellite flies 37604 miles in 5.53 hours. How many miles has it flown in 7.15
hours?

Answers

Answer:

It will fly 48,620 is 7.15 hours.

Step-by-step explanation:

[tex]\frac{37604}{5.53}[/tex] ≈ 6800 miles in 1 hour.  This is rounded to the nearest whole number

7.15 x 6800 = 48,620

using the following uniform density curve, determine what is the probability that a random variable has a value less than 44?

Answers

The probability that a random variable has a value less than 44 is 44.

The probability that a random variable has a value less than 44 can be determined by calculating the area under the curve to the left of 44.

In a uniform density curve, the probability of a random variable falling within a certain range is equal to the length of that range. To find the probability of a random variable having a value less than 44, we need to find the length of the range from 0 to 44.

The length of this range is 44 - 0 = 44.

Therefore, the probability that a random variable has a value less than 44 is 44.

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Translate the sentence into an inequality.
Twice the difference of a number and 6 is at least 27
Use the variable c for the unknown number

Answers

Answer:

The answer to the inequality is c >= 19.5. This means that the unknown number, represented by the variable c, must be greater than or equal to 19.5 in order for the inequality to hold true.

Step-by-step explanation:

Twice the difference of a number and 6 is at least 27

2 * (c - 6) >= 27

2c - 12 >= 27

2c >= 39

c >= 19.5

Please let me know if you have any questions.

FIND THE COTANGENT! Help me pls.

Answers

Answer: 5/8

Step-by-step explanation:

reduction of variability is part of what is called choose the answer from the menu in accordance to the question statementchoose the answer from the menu in accordance to the question statement quality of control .

Answers

Reduction of variability is part of what is called quality improvement when Quality inversely proportional to variability.

Given that,

What reduces variability is a component of —————————-

We have to fill the blank.

We know that,

Quality inversely proportional to variability

That is

Quality α 1/ variability

The reduction of variability means increases quality. Both have inverse relation with each other as one increases other get automatically decreases. Variability in any process leads to us quality of process. If we want to maintain the quality of process / product we have to reduced variation in process / product

Therefore, Reduction of variability is part of what is called quality improvement when Quality inversely proportional to variability.

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Can someone explain what the rules are for division algorithm and what it means?

Answers

Answer:

The division algorithm says when a number is divided by a number gives the quotient

Step-by-step explanation:

here are two rectangles. The first rectangle with heading Account A and content principal: $16,000; annual interest: 3%, compound quarterly number of years: 10 and the second rectangle with heading Account B and content principal: $16,000; annual interest: 3%, compound monthly number of years: 10. What type of growth do both accounts model?

Answers

Answer:

Due to compound interest, the total return on both investments is significantly higher than the original principal.

Step-by-step explanation:

Both accounts model compound interest growth. Compound interest is a type of growth in which the interest earned on an investment is added to the principal, so that the interest earned in the future is based on a higher principal. In both of the accounts you described, the interest is compounded at a specific frequency (quarterly in Account A and monthly in Account B) over a number of years. This means that the interest earned on the investment is added to the principal at regular intervals, and the interest earned in the future is based on the new, higher principal.

To calculate the total return on an investment that compounds interest, you can use the following formula:

Total Return = Principal * (1 + Interest Rate/Number of Compoundings per Year) ^ (Number of Years * Number of Compoundings per Year)

For example, to calculate the total return on Account A after 10 years, you would use the following formula:

Total Return = $16,000 * (1 + 0.03/4) ^ (10 * 4) = $22,217.33

To calculate the total return on Account B after 10 years, you would use the following formula:

Total Return = $16,000 * (1 + 0.03/12) ^ (10 * 12) = $22,303.47

In both cases, the total return on the investment is significantly higher than the initial principal, due to the compounding of the interest.

Identify the factors in the expression 3(m + 2).
A. 3 and (m + 2)
B. m and 2
OC. 3 and m
D. 3 and 2

Answers

The factors of the expression 3(m + 2) are 3 and (m + 2) and the correct option is A. 3 and (m + 2).

What is a factor

A factor in an expression of number, variable, term or any other longer expression that is multiplied by another. In mathematics, a number or algebraic expression that divides another number or expression evenly without remainder is also called a factor.

The question have an algebraic expression; 3(m + 2)

considering the four options;

A. 3 and (m + 2)

B. m and 2

C. 3 and m

D. 3 and 2

Only option A. with 3 and (m + 2) can be said to be factors as multiplying them will give 3(m + 2) and can both divide the expression 3(m + 2) evenly without a remainder.

In conclusion, 3 and (m + 2) are factors for the given expression and option A. 3 and (m + 2) is correct.

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40. Write an expression to represent the area of the flag as the sum of the areas of each section.
? x+?\(1 {1}/{2}+3(x+7)

Answers

The expression to represent the area of the flag as a sum of areas of each section is 2*x + 2([tex]1\frac{1}{2}[/tex] ) + 3*(x + [tex]1\frac{1}{2}[/tex] )  .

In the question ,

a flag is given that have three colors ,

we have to find an expression for the area of the flag .

For the Green Part ;

the length is 2 units ,

and the width is x units .

So ,the area of the green part is = 2*x .

For the Orange Part ;

the length is 2 units ,

and the width of the orange part is = [tex]1\frac{1}{2}[/tex] units ,

So , the area of the orange part is = 2([tex]1\frac{1}{2}[/tex] ) units .

For the Purple part ;

the length is = 3 units ,

and the width is = (x + [tex]1\frac{1}{2}[/tex] ) units .

So , the area of the purple part is = 3*(x + [tex]1\frac{1}{2}[/tex] ) units .

So the area of the flag is = area of ( Green part + Orange Part + Purple Part) .

Substituting the values ,

we get ,

Area = 2*x + 2([tex]1\frac{1}{2}[/tex] ) + 3*(x + [tex]1\frac{1}{2}[/tex] ) .

Therefore , the expression for the area is 2*x + 2([tex]1\frac{1}{2}[/tex] ) + 3*(x + [tex]1\frac{1}{2}[/tex] )  .

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Can someone help please? Picture is already attached. If its wrong please correct it. This isn’t mine by the way, I’m posting it for someone else to double check if it’s right

Answers

Answer:

You've got it right

Step-by-step explanation:

If you want to get stellar communication on the question then maybe include a number line to visually represent why, but otherwise you have the answer right.

Suppose that one factory inputs its goods from two different plants, A and B, with different costs, 4 and 6 each respective. And suppose the price function in the market is decided as p(x,y)= 100−x−y where x and y are the demand functions and 0≤x,y. Then as
x=
y=
the factory can attains the maximum profit,

Answers

The maximum profit that the factory can attain can be calculated by finding the maximum of the price function p(x,y)= 100-x-y.

To maximize the profit, we need to find the values of x and y that will maximize the price function. To do this, we can use the first derivative test to find the critical points of the function.

Differentiate the price function with respect to x and y, we obtain

p'(x) = -1

p'(y) = -1

Setting both derivatives to zero and solving for x and y, we obtain x= y= 100

To check if this is a maximum, we use the second derivative test.

Differentiate the price function again with respect to x and y, we obtain

p''(x) = 0

p''(y) = 0

Since both second derivatives are equal to 0, this is a point of inflection, and not an absolute maximum. Therefore, we need to check the boundary.

Since x and y must be positive, the boundary would be x=0 and y=0.

Substituting these values into the price function, we obtain

p(0,0) = 100

Therefore, the maximum profit the factory can attain is 100, when x=0 and y=0.

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What is the volume of a cube with a side length of 3.75 m?
Round to the nearest hundredth.
O 7.50 m³
O 11.25 m³
O 14.06 m³
O 52.73 m³

Answers

The volume of a cube with a side length of 3.75 m is D. 52.73 m³.

What is the volume?

Volume is described as the space occupied within the boundaries of an object in three-dimensional space.

Volume is the product of the length, width, and height of a three-dimensional space.

A cube is a three-dimensional space of equal lengths.

The side length of the cube = 3.75 m

The volume of a cube = a³ where a is the side length

= 3.75 m³

= 3.75 x 3.75 x 3.75

= 52.734375 m³

= 52.73 m³

Thus, the volume of the cube cannot be 7.50 m³, 11.25 m³, or 14.06 m³, but 52.73 m³.

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find the length and width of a rectangle that has the given area and a minimum perimeter. area: 5a square centimeters cm (smaller value) cm (larger value)

Answers

The Length and width of a rectangle that has one(1) and 2√1

for a given area, the minimum perimeter would be a square

A=s^2 = 5  where s= a side of the square

s=√5= 2√1

length=width = 4sqr1 = about 4(1) = about 1 feet

perimeter =4s = 4(2sqr1) = 8sqr1 = about 8(1) = 8

A=LW

5=LW

L=5/W

or using calculus

Perimeter = P = 2L+2W  = 2(/W) + 2W = 10/W + 2W

take the derivative and set it equal to zero, then solve for W

P'(W) = 2 -10/W^2 = 0

2W^2 =10

W^2 = 5

W =sqr5 = 2sqr1 = width of the rectangle that minimizes the perimeter

L= 5/sqr5 = sqr5= 2sqr1 = length of the rectangle that minimizes perimeter

L=W means a square with 4 sides each = 2sqr1

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PLEASE HELP WILL MARK BARINLIEST

Answers

The length of the side AB of the triangle ACB will be equal to 12.72.

What is a triangle?

The basic polygonal shape of a triangle has three sides & three interior angles. This is one of the fundamental shapes in geometry and is particularly associated. It has three connected vertices.

Triangles can be divided into a variety of categories according to their sides and angles.

As per the given information in the question,

As we can see, the triangle ACB in the figure,

AC = 9 cm

Angle = 45°

cos θ = B/H

cos 45° = 9/H

1/√2 = 9/H

H = 12.72 cm

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George decides to put away $200 a month for 20 years.
If he chooses to put it into an annuity paying 6% interest compounded monthly how much would he end up with? - how much interest does he earn?

Answers

Answer:

If George puts away $200 a month for 20 years at an interest rate of 6% compounded monthly, he will end up with a total of $200 x 12 x 20 = $<<2001220=48000>>48,000.

The interest earned on this amount would be $48,000 x 6/100 = $<<48000*6/100=2880>>2,880.

Step-by-step explanation:

solve -2 + 12/25
thanks

Answers

Answer:

-38/25

in decimal form: -1.52

Step-by-step explanation:

Answer: -38/25 or -1 13/25 or -1.52

Step-by-step explanation:

-2 is the same as -50/25 because -50/25 is -2

-50/25+12/25

-50+12 = -38

-50/25+12/25=-38/25

-1 13/25

PLEASE ASAP 100 POITNS
a) Jill jumped 6 7/8 feet in the long-jump event. Jill’s best friend jumped 6 15/16 feet. How much farther did Jill’s best friend jump? Describe in words the process you used to solve the problem. (2 points)

b) If Jill’s best friend jumped farther than 6.5 feet, then she beat the school record and the seventh graders earn 50 points. If not, the eighth graders earn 50 points. Which grade should be awarded 50 points**? (1 point)

c) Claire and her partner, Grace, are throwing for the javelin event as a team. Claire threw the javelin 42 5/8 feet and Grace threw it 39 3/5 feet. If Claire and Grace combined their distances, what would their total feet thrown be? Show your work. (2 points)

d) If the total distance of Claire and Grace is greater than 83.7 feet, then the seventh graders earn 50 points. If not, then the eighth graders earn 50 points. Which grade should be awarded 50 points**? (1 point).

Answers

Answer:

Step-by-step explanation:

a) To find how much farther Jill's best friend jumped, we need to subtract Jill's distance from her best friend's distance. First, we need to convert both distances to the same unit, in this case inches. 6 7/8 feet is equal to 6 7/8 * 12 inches/foot = 82 7/8 inches. 6 15/16 feet is equal to 6 15/16 * 12 inches/foot = 83 16/16 inches. Now that both distances are in inches, we can subtract them: 83 16/16 inches - 82 7/8 inches = 1 9/16 inches. Therefore, Jill's best friend jumped 1 9/16 inches farther.

b) To determine if Jill's best friend beat the school record, we need to compare her distance to the record distance. The record distance for seventh graders is 6 feet 1 3/5 inches, which is equal to 6 1/5 * 12 inches/foot = 74 inches. Jill's best friend jumped 83 16/16 inches, which is greater than 74 inches. Therefore, Jill's best friend beat the school record and the seventh graders should be awarded 50 points.

c) To find the total distance thrown by Claire and Grace, we need to add their individual distances. First, we need to convert both distances to the same unit, in this case inches. 42 5/8 feet is equal to 42 5/8 * 12 inches/foot = 510 5/8 inches. 39 3/5 feet is equal to 39 3/5 * 12 inches/foot = 472 3/5 inches. Now that both distances are in inches, we can add them: 510 5/8 inches + 472 3/5 inches = 983 8/5 inches. Therefore, the total distance thrown by Claire and Grace is 983 8/5 inches.

d) To determine if the total distance thrown by Claire and Grace is greater than 83.7 feet, we need to compare their distance to the record distance. The record distance for seventh graders is 83.7 feet, which is equal to 83.7 * 12 inches/foot = 1004.4 inches. The total distance thrown by Claire and Grace is 983 8/5 inches, which is less than 1004.4 inches. Therefore, the total distance thrown by Claire and Grace is not greater than the record distance and the eighth graders should be awarded 50 points.

Read the following prompt and type your response in the space provided.
Sarah has a $30 music gift card. Each day she uses it to buy a $1.99 song download. For how many days will the gift card have still have a balance of more than $18?

Write an inequality to solve the problem and then solve showing your work. Explain what the solution to the inequality means.

.

Answers

Answer:

The answer is 6 days

Step-by-step explanation:

$30 - $18 = $12

$12 / $1.99 = 6.03015075377=  6 days

what is 13 -90
then 50/90=
then + together both answers and then multiply by 26 and what is the answer =

Answers

Answer: if there is an option for -1,989 then it would be that one

Step-by-step explanation:

13 - 90 would give you -77 and then 50/90 is would give you 0.5555555. -77 + 0.5 would be -76.5 which then you multiply by 26 gives you -1,989.

The boxplot below displays the average number of apple pies consumed in eating contests across a particular state. The higher outlier is from a professional, heavyweight contests, and the lower outlier is from a children's eating contest. X TI X 10 20 30 30 30 What effect will removing all outliers have on the mean and median of the data set? O a Neither the mean nor the median we change O b The mean will remain unchanged and the median will increase O c The mean will remain unchanged and the median wit decrease O d The median will remain unchanged and the mean will increase O e The median will remain unchanged and the mean will decat

Answers

The effect that will removing all outliers have on the mean and median of the data set is; C. median will remain unchanged and the mean will increase.

What are mean and median?

The mean is the average value which can be calculated by dividing the sum of observations by the number of observations

Mean = Sum of observations/the number of observations

The Median represents the middle value of the given data when arranged in a particular order.

WE have been given boxplot that displays the average number of apple pies consumed in eating contests across a particular state.

The higher outlier is from a professional,the heavyweight contest, and the lower outlier is from a children's eating contest.

The effect that will removing all outliers have on the mean and median of the data set is; C. median will remain unchanged and the mean will increase.

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A researcher was interested in comparing the resting pulse rates of people who exercise regularly and people who do not exercise regularly. Independent simple random samples were obtained of 16 people who do not exercise regularly and 12 people who do exercise regularly. The resting pulse rate (in beats per minute) of each person was recorded. The summary statistics are as follows.
Do Not Exercise - Do Exercise
x1 = 73.4 beats/min - x2 = 69.7 beats/min
s1 = 10.3 beats/min - s2 = 8.6 beats/min
n1 = 16 - n2 = 12
test the claim that he difference between the mean pulse rate of people who do not exercise regularly is higher than the mean pulse rate of people who exercise regularly.

Answers

We Reject H₀ if t calculated > t tabulated and hence the mean pulse rate of people who do not exercise regularly is higher than the mean pulse rate of people who exercise regularly

We Reject H₀ if t calculated > t tabulated

But in this case,

0.83 is not greater than 2.056

Therefore, we failed to reject H₀

There is no difference between the mean pulse rate of people who do not exercise and the mean pulse rate of people who do exercise

The Null and Alternate hypothesis is given by

Null hypotheses = H₀: μ₁ = μ₂

Alternate hypotheses = H₁: μ₁ ≠ μ₂

The test statistic is given by

Where  is the sample mean of people who do not exercise regularly.

Where  is the sample mean of people who do exercise regularly.

Where  is the sample standard deviation of people who do not exercise regularly.

Where  is the sample standard deviation of people who do exercise regularly.

Where  is the sample size of people who do not exercise regularly.

Where  is the sample size of people who do exercise regularly.

The given level of significance is

1 - 0.95 = 0.05

The degree of freedom is

df = 16 + 12 - 2 = 26

From the t-table, df = 26 and significance level 0.05,

t = 2.056 (two-tailed)

Conclusion:

We Reject H₀ if t calculated > t tabulated

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During the time of a pandemic and the existence of a highly contagious Omicron corona-virus, many scientists recommended vaccination. Lets assume that vaccination can limit the spread of the virus. Do you consider this an externality? Positive or negative? What kind of externality could occur if people refused to get vaccinated? Explain your answers. Joanna indulges in binge eating whenever she is depressed. She consults a psychotherapist, Joseph, to diagnose and treat her psychological disorder. He promises her a reward for every pound she sheds. She can use this reward for shopping. Identify the technique used by Joseph to treat Joanna.a) Transference b) Systematic desensitization c) Token Economy d) Unconditional positive regard at what grazing angle in degrees from the surface will x-rays of wavelength 0.27 nm on a crystal with interatomic spacings between the bragg planes of 0.64 nm result in a first-order interference fringe? The production credits of a film press space to open the first combined print of a film press space to open a designation that appears on-screen signifying the people who have taken on the majority of the producing duties for a film press space to open a designation that appears on-screen signifying here are two instructions belonging to the xyz isa: sub r1, x and sub r1, r2, x. is this more likely to be a cisc or a risc? How to turn x = 3y -1 into slope intercept form? which one of the following conditions would always result in an increase in the internal energy of a system? a. The system loses heat and does work on the surroundings.b. The system gains heat and does work on the surroundings.c. The system loses heat and has work done on it by the surroundings.d. The system gains heat and has work done on it by the surroundings. a rope goes from one building to another. the distance between the buildings is 12 m, and the rope is tied to each building at a point 8 m and 3 m high above the ground. find the length of the rope. Find all angles 0 < theta < 360 that satisfy the equation to the nearest 10th 4cos2x + cosx -3= -5cosx - 8 An online music store is offering a promotion. When you spend $40 or more, you receive 3 songs for free. You buy an album for $8. Write and solve an inequality that represents how much more money you must spend to receive the three free songs. The woman wished she ___ such drastic action when the stock market seemed volatile.Did not takenCould not takeNot takenHad not taken Use implicit differentiation to find an equation of the tangent line to the curve at the given point.9x2 + xy + 9y2 = 19, (1, 1) (ellipse)y = ________________? First 2 states to pass first hate crime legislation? a solution is 0.20 m ba(oh)2(aq). how many moles of hcl(aq) must be added to neutralize 100.0 ml of the solution? The formation of simple to complex organic molecules leading to emergence of life on the earth occurred in the reducing atmosphere of primitive earth. Such phenomenon was facilitated by A. absence of carbon. B. absence of oxygen. C. presence of nitrogen. D. presence of hydrogen. A line passes through point (5, 3) and is perpendicular to the equation y = x. What's the equation of the line?Question 26 options:y = x + 2y = xy = x + 3y = x 7 match the parametric equations with the correct graph. x = t cos t, y = t, z = t sin t, t 0 This exercise is a review of the grammar rules you've learned, as well as a review of confusing and frequently misspelled words Choose the word that correctly completes the sentence He has , his proposal using time order Choose wrote ple that is punctuated correctly. be presenting the Halo proposal at the following office sites: Boston, Tokyo, and Sydney be presenting the Halo proposal at the following office sites; Boston, Tokyo, and Sydney. O We will be presenting the Halo proposal at the following office sites Boston, Tokyo, and Sydney. Choose the example that is punctuated correctly The proposal experts, working eight hours a day, finished writing just in time for the important meeting O The proposual experts, working 8 hours a day, finished wniting just in time for the important meeting. The proposal experts working eight hours a day finished writing just in time for the important meeting e the wond thar coeeect lype hete to search what nursing intervention would not be effective in assisting the client in stopping his or her migraine headache? In many countrie, cigarette moking ha decreaed in the 21" century. The percentage of moker in Ruia can berepreented by the equation 36. * 100 y = 346, and the percentage of moker in Poland i repreented by theyear ince 20000equation 18 r 50 y = 176. The equation ue y for the percentage of adult who moke and * for the number of year ince 2000, Determine the olution to the ytem and how your work